prime of the form

(a+12)^b-c

with c prime and
d=divisors(a)
s=sum(j=1,length(d)-1,d[j])
a=s-12

sample
(10^10+518+12)^1024-3361
a=10^10+518
b=2^10
c=3361 prime
d=[1, 2, 3, 6, 1666666753, 3333333506, 5000000259, 10000000518]
s=10^10+530

PARI GP ispseudoprime

To be completed...